Full-Scale Bounds Estimation for the Nonlinear Transient Heat Transfer Problems with Interval Uncertainties

2021 ◽  
pp. 2150026
Author(s):  
Ruifei Peng ◽  
Haitian Yang ◽  
Yanni Xue
Keyword(s):  
Heat Transfer ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Transient Heat Transfer ◽  
High Fidelity ◽  
Interval Scale ◽  
Nonlinear Transient ◽  
Transfer Problems ◽  
Derivatives Of

A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the interval scale is relatively large, an optimization-based approach in conjunction with a dimension-adaptive sparse grid (DSG) surrogate is developed for the bounds estimation of temperature, and the heavy computational burden of repeated deterministic solutions of nonlinear transient heat transfer problems can be efficiently alleviated by the DSG surrogate. A temporally piecewise adaptive algorithm with high fidelity is employed to gain the deterministic solution of temperature, and is further developed for recursive adaptive computing of the first and second-order derivatives of temperature. Therefore, the implementation of Taylor series expansion and the construction of DSG surrogate are underpinned by a reliable numerical platform. The parallelization is utilized for the construction of DSG surrogate for further acceleration. The accuracy and efficiency of the proposed approaches are demonstrated by two numerical examples.

Approximate Solution of a Class of Radiative Heat Transfer Problems

2000 ◽  
Vol 122 (3) ◽  
pp. 606-612 ◽  
Author(s):  
H. Qiao ◽  
Y. Ren ◽  
B. Zhang
Keyword(s):  
Heat Transfer ◽  
Approximate Solution ◽  
Series Expansion ◽  
Taylor Series ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Transfer Problems ◽  
Series Expansion Method

An approximate solution is presented for a class of radiative heat transfer problems within enclosures having black or diffuse-gray surfaces based on a modified Taylor series expansion method; such radiative transfer problems are generally represented by integral equations. The approach avoids use of any boundary/initial conditions associated with the original Taylor series expansion method and leads to an approximate solution in a simple closed form to the radiant integral equations, which can be computed straightforwardly on a modern personal computer using symbolic computing codes such as Maple. The method can be effectively and efficiently applied to deal with enclosures involving more than one or two surfaces, for which direct numerical integration may be subject to instability, or require an excessive amount of computation. The computed numerical results for representative thermal problems are in excellent agreement with those obtained by other numerical approaches. [S0022-1481(00)00203-6]

A Tabular Taylor Series Expansion Method for Fast Calculation of Steam Properties

1997 ◽  
Vol 119 (2) ◽  
pp. 485-491 ◽  
Author(s):  
K. Miyagawa ◽  
P. G. Hill
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
International Association ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
The State ◽  
Steam Power ◽  
Direct Use ◽  
Derivatives Of ◽  
Plane Grid

A new method is proposed for rapid and accurate calculation of steam properties in the regions of the state plane of greatest importance to the steam power industry. The method makes direct use of the derivatives of that Helmholtz function that is the best available wide-ranging scientific formulation of the properties of steam. It is rapid because, with a six-term Taylor series expansion, it uses property values and derivatives evaluated once and for all from the Helmholtz function and stored in tables pertaining to an optimized state plane grid configuration. The method eliminates the need for iterative property calculations and is amenable to any region of the state plane. For properties in the ranges of temperature from 0 to 800°C and pressure from 0 to 100 MPa the core memory requirement for three functions of any given pair of independent properties is less than 1 Mb. With this memory allocation it is possible everywhere in the stated range to satisfy the specific volume and enthalpy tolerances specified by the International Association for the Properties of Water and Steam. An optimized formulation of the method is demonstrated in this paper for enthalpy, entropy, and volume functions of pressure and temperature in the superheat region.

Computation of Eigenvalues and Eigenvectors of a Mistuned Bladed Disk

2006 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Eigenvalues And Eigenvectors ◽  
Numerical Examples ◽  
Bladed Disk ◽  
Repeated Eigenvalues ◽  
Derivatives Of ◽  
Computation Of Eigenvalues

This paper deals with fundamental aspects of variations in eigenvalues and eigenvectors of a bladed disk due to mistuning. First, the existence of derivatives of repeated eigenvalues and corresponding eigenvectors is thoroughly examined. Next, an algorithm is developed to compute these derivatives. It is shown how a Taylor series expansion can be used to efficiently compute eigenvalues and eigenvectors of a mistuned system. This methodology is developed for perturbations in both repeated and unrepeated eigenvalues of the tuned system. Lastly, numerical examples are presented.

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

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